System, method and computer-accessible medium for joint magnetic resonance-positron emission tomography reconstruction using multi-sensor compressed sensing

ABSTRACT

An exemplary system, method and computer-accessible medium for generating a magnetic resonance (MR) image(s) and a positron emission tomography (PET) image(s) of a tissue(s) can be provided, which can include, for example, receiving information related to a combination of MR data and PET data as a single data set, separating the information into at least two dimensions, at least one first of the dimensions corresponding to the MR data and at least one second of the dimensions corresponding to the PET data, and generating the MR image(s) and the PET image(s) based on the separated information.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application relates to and claims priority from U.S. patentapplication No. 61/984,374, filed on Apr. 25, 2014, the entiredisclosure of which is incorporated herein by reference.

FIELD OF THE DISCLOSURE

The present disclosure relates generally to a magnetic resonance imaging(“MRI”), and more specifically, to exemplary embodiments of an exemplarysystem, method and computer-accessible medium for providing a jointmagnetic resonance (“MR”)-positron emission tomography (“PET”)reconstruction, for example, using multi-sensor compressed sensing.

BACKGROUND INFORMATION

Current MR-PET scanners enable simultaneous acquisition of PET and MRdata. (See, e.g., Reference 1). However, in the current data processingpipeline, image reconstruction is performed separately for MR and PETdata, and the results are only combined at the visualization stage. PETimages are reconstructed using the Expectation Maximization (“EM”)procedure (see, e.g., Reference 2) or one of its variants, whereas MRdata is reconstructed either using an inverse Fourier transform (e.g., aconventional transform) or an iterative procedure in cases such asparallel imaging or compressed sensing.

Thus, it may be beneficial to provide an exemplary system, method andcomputer-accessible medium for joint MR-PET reconstruction which canovercome at least some of the deficiencies described herein above.

SUMMARY OF EXEMPLARY EMBODIMENTS

An exemplary system, method and computer-accessible medium forgenerating a magnetic resonance (MR) image(s) and a positron emissiontomography (PET) image(s) of a tissue(s) can be provided, which caninclude, for example, receiving information related to a combination ofMR data and PET data as a single data set, separating the informationinto at least two dimensions, a first of the dimensions corresponding tothe MR data and second of the dimensions corresponding to the PET data,and generating the MR image(s) and the PET image(s) based on theseparated information.

In some exemplary embodiments of the present disclosure, the dimensionscan be at least four dimensions. The dimensions can be generated basedon an optimization procedure. Sharing of the MR data and the PET datawith one another can be substantially prevented when the

MR data and the PET data to not match. In addition, an exemplarysparsifying transform can be applied to the MR image(s) to removeundersampling artifacts from the MR image(s). An initialthree-dimensional PET image volume can be generated from the PET databased on an expectation maximization (EM) procedure. The PET image(s)can be updated using the EM procedure. An initial estimation of the MRdata can be generated by applying an adjoint of an MR forward operatorto the MR data.

In another exemplary embodiment of the present disclosure can be anexemplary system, method and computer-accessible medium for generating afirst image(s) and a second image(s) of a tissue(s), which are differentfrom one another, which can include, receiving combined informationrelated to a combination of first imaging information and second imaginginformation as a single data set, separating the combined informationinto at least two dimensions into separated information, a first of thedimensions corresponding to the first imaging information and a secondof the dimensions corresponding to the second imaging information, andgenerating the first image(s) and the second image(s) based on theseparated information. The first imaging information can be from orbased on a first imaging modality, the second imaging information can befrom or based on a second imaging modality and the first imagingmodality can be different than the second imaging modality. The firstimaging modality and/or the second imaging modality can be related to amagnetic resonance imaging modality, a positron emission tomographyimaging modality, a single-photon emission computed tomography modalityor an optical modality.

According to some exemplary embodiments of the present disclosure, thefirst imaging information can be or can include magnetic resonance (MR)data, and the second imaging information can be or can include positronemission tomography (PET) data. The first image(s) can be a MR image(s),and the second image(s) can be a PET image(s).

For example, the computer arrangement can be further configured to atleast substantially prevent sharing of the first imaging information andthe second imaging information with one another when the first imaginginformation and the second imaging information to not match. A sparsityparameter can be applied to the first imaging information to removeundersampling artifacts from the first imaging information. An initialthree-dimensional image volume from the second imaging information canbe generated based on an expectation maximization (EM) procedure, andthe second image(s) can be updated using the EM procedure.

In certain exemplary embodiments of the present disclosure, the MR datacan include measured k-space raw data. The first image(s) and the secondimage(s) can be generated based on an incoherence of artifacts in theseparated information and/or based on a comparison of the separatedinformation. The first image(s) can be generated temporally before thesecond image(s), and the second image(s) can be generated based on thefirst image(s)

These and other objects, features and advantages of the exemplaryembodiments of the present disclosure will become apparent upon readingthe following detailed description of the exemplary embodiments of thepresent disclosure, when taken in conjunction with the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Further objects, features and advantages of the present disclosure willbecome apparent from the following detailed description taken inconjunction with the accompanying Figures showing illustrativeembodiments of the present disclosure, in which:

FIG. 1 is a group of exemplary diagrams and images illustrating aconventional magnetic resonance-positron emission tomography procedure;

FIG. 2 is a group of exemplary diagrams and exemplary imagesillustrating a magnetic resonance-positron emission tomography procedureaccording to an exemplary embodiment of the present disclosure;

FIG. 3 is an exemplary flow diagram illustrating an exemplaryreconstruction pipeline according to an exemplary embodiment of thepresent disclosure;

FIG. 4 is a set of exemplary images illustrating a conventionalreconstruction procedure, and an individual MR and PET nonlinearcompressed sensing reconstruction procedure compared to the exemplaryreconstruction procedure;

FIG. 5 is a set of exemplary images illustrating image quality of theexemplary reconstruction procedure according to an exemplary embodimentof the present disclosure;

FIG. 6A is an exemplary image of a cross-sectional profile of a cranialslice according to an exemplary embodiment of the present disclosure;

FIG. 6B is an exemplary graph illustrating cross-sectional profile plotsaccording to an exemplary embodiment of the present disclosure;

FIG. 7 is a set of exemplary images illustrating a pseudorandomone-dimensional subsampling pattern according to an exemplary embodimentof the present disclosure;

FIG. 8 is a flow diagram of an exemplary method for generating a firstimage and a second image of tissue according to an exemplary embodimentof the present disclosure; and

FIG. 9 is an illustration of an exemplary block diagram of an exemplarysystem in accordance with certain exemplary embodiments of the presentdisclosure.

Throughout the drawings, the same reference numerals and characters,unless otherwise stated, can be used to denote like features, elements,components or portions of the illustrated embodiments. Moreover, whilethe present disclosure will now be described in detail with reference tothe figures, it is done so in connection with the illustrativeembodiments and is not limited by the particular embodiments illustratedin the figures and the appended claims.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

FIG. 1 illustrates an exemplary diagram of a conventional MR-PETprocedure and an illustration of a conventional device to perform suchprocedure. In particular, MR and PET data can be acquired at the sametime on the same system 105, and can then be separated into twodifferent processing pipelines (e.g., pipelines 110 and 115). PET images120 can be reconstructed using Filtered Backprojection (“FBP”),expectation maximization (“EM”) or ordered subset expectationmaximization (“OSEM”) (see, e.g., Reference 4) at procedure 125, and theMR data 130 can be conventionally reconstructed using an inverse Fouriertransform at procedure 135. After each set of images can bereconstructed (e.g., images 140 and 145), the images can then be fusedtogether for visualization at procedure 150.

In contrast to the procedure shown in FIG. 1, the exemplary system,method and computer-accessible medium according to an exemplaryembodiment of the present disclosure, as illustrated in FIG. 2, canacquire MR and PET data using an imaging system 205 (e.g., MR data 210and PET data 215) as one single data set and jointly reconstruct the MRimage 225 and PET image at procedure 220. The exemplary images can thenbe fused together for visualization in the same way as in the prior artprocedure above. By treating the two imaging modalities as additionaldimensions of a single dataset, the exemplary method can reconstruct afour-dimensional (“4D”) data set by an exemplary solution of thefollowing exemplary optimization problem, where for example:

$\begin{matrix}{{\min {{{E\left( x_{MR} \right)} - k}}_{2}^{2}} + {\sum\limits_{j = 1}^{J}\; \left( {\left( {A\left( x_{PET} \right)} \right)_{j} - {f_{j}{\log \left( {A\left( x_{PET} \right)} \right)}_{j}}} \right)} + {\lambda {{{\begin{matrix}{\Psi \left( x_{MR} \right)} \\{\Psi \left( x_{PET} \right)}\end{matrix}}_{2}}_{1}.}}} & (1)\end{matrix}$

where xMR can be a 3D MR image volume, k can be MR k-space raw data, Ecan map the MR images to 3D k-space and can include coil sensitivitymodulation. Mapping the 3D image volume xPET to the sinogram data f. jcan be indices of the PET lines of response, and J can be the totalnumber of PET lines of response. A can be a regularization parameter andΨ can be the sparsifying transform. Eq. (1) can include three distinctterms. The first term can enforce data fidelity of the current solutionwith the acquired MR raw data. The second term can enforce PET dataconsistency. Here the Kullback-Leibler divergence can be used as adistance measure instead of the 12-norm because of the Poisson noisedistribution in PET as opposed to Gaussian noise in MR raw data. Thethird term can be the joint sparsity, which can be a generalization ofthe 11-norm to the case of multiple image sets. Two different norms canbe needed for the joint sparsity term. The inner 12-norm can combine thetransformed MR and PET signal intensities into combined sparsecoefficients while the outer 11-norm can sum the combined coefficientsand enforces sparsity of the solution. An exemplary definition of theinner 12-norm in Eq. (2) can be given, for example, as follows:

$\begin{matrix}{{\begin{matrix}{\Psi \left( x_{MR} \right)} \\{\Psi \left( x_{PET} \right)}\end{matrix}}_{2} = \sqrt{{\Psi \left( x_{MR} \right)}^{2} + {\Psi \left( x_{PET} \right)}^{2}}} & (2)\end{matrix}$

Iterative soft thresholding (28) can be used as the numerical method tofind a minimizer of the cost functional in Eq. (1). The reconstructionprocedure is illustrated in FIG. 3.

As shown in FIG. 3, initial estimates x⁰ _(MR) (e.g., procedure 310) andx⁰ _(PET) (e.g., procedure 305) can be selected. For MR, this can beeither an all zeroes image or the application of the adjoint of the MRoperator to the measured k-space raw data k. In the case of PET, an allones image can be used. Current estimates of MR (e.g., procedure 320)and PET (e.g., procedure 315) images can then be used in a softthresholding procedure (e.g., procedure 355) after application of thesparsifying transform Ψ. The output of this exemplary procedure can beupdated estimates of MR (e.g., procedure 340) and PET (e.g., procedure345) images, which can then be subjected to data consistency conditionsdescribed below.

The exemplary PET forward operator A, used in the PET data fidelityprocedure (e.g., procedure 350), can include two components X and C. Xcan represent the line model whereas C can be a blurring operator, whichcan be used to model the point spread function of the scanner.N=1/(XC)*e−Xμ can account for geometric normalization and attenuationcorrection. The division can be performed on a voxel by voxel basis. μcan represent the linear attenuation coefficient. Estimates forscattered and random coincidences (e.g., fr and fs) can be added to theforward projection, and can be corrected for attenuation accordingly.Crystal normalization can also accounted for, but can be been omitted inthe formula for the sake of simplicity.

Consistency with the acquired MR raw data k can be enforced in the MRimage update procedure (e.g., procedure 335. It should be noted thatboth the MR and PET image updates can follow directly from the twodifferent data fidelity distance measures in Equation 1 due to thedifferent noise statistics of the two modalities. The whole iterationsequence can then be repeated until the defined number of iterations canbe reached (e.g., procedure 325). The output of the complete procedurecan be a set of MR and PET images (e.g., procedure 330) that canminimize the cost functional from Equation 1.

Initial estimates x⁰ _(MR) and x⁰ _(PET) can be selected. For MR, thiscan be either an all zeroes image or the application of the adjoint ofthe MR operator to the measured k-space raw data k. In the case of PET,an all ones image can be used. Current estimates of MR and PET imagescan then be used in a soft thresholding step after application of thesparsifying transform Ψ.

The PET forward operator A used in the PET data fidelity procedure caninclude the two components X and C. X can represent the line modelwhereas C can be a blurring operator, which can be used to model thepoint spread function of the scanner. N=1/(XC)*e^(−Xμ) can account forgeometric normalization and attenuation correction. The division can bedone on a voxel by voxel basis. μ can represent the linear attenuationcoefficient. Estimates for scattered and random coincidences (f_(r) andf_(s)) can be added to the forward projection, and can be corrected forattenuation accordingly. Crystal normalization can also be taken intoaccount although such consideration can be for the sake of simplicity.

Consistency with the acquired MR raw data k can be enforced orfacilitated in the MR image update procedure. For example, both the MRand PET image updates can follow directly from the two different datafidelity distance measures in Eq. (1) due to the different noisestatistics of the two exemplary modalities. The whole iteration sequencecan then be repeated until the defined number of iterations can bereached.

An exemplary advantage of the exemplary procedure, according to anexemplary embodiment of the present disclosure, can be that while MR andPET can provide unique and independent information, they can be based onthe same anatomy. High resolution MR information can be used to enhancethe PET reconstruction. In addition, as MR artifacts, like aliasing orgeometrical distortions, may not be present in the PET image, adedicated reconstruction can exploit the incoherence of artifacts in thejoint space. The exemplary system, method and computer-accessible mediumcan therefore facilitate a reconstruction of a higher resolution PETdata, for example, without compromising the SNR. Examples of theexemplary reconstruction are illustrated in FIGS. 4 and 5.

An exemplary feature of the exemplary system, method andcomputer-accessible medium can be that features that can appearexclusively in only one of the two modalities may not be transferred tothe second modality. Thus, the exemplary system, method andcomputer-accessible medium can be robust against this because it mayonly enforce joint structures. This is illustrated in the example shownin FIG. 5. An interesting exemplary feature of this particular datasetcan be the distinct hyper-intense lesion in MR in the cranial slice(e.g., row 505) where no PET tracer accumulation occurs (highlighted byarrows 510). In contrast, the caudal slice (e.g., row 515) includessubcortical gray matter regions (e.g., caudate and thalamus), with nosubstantial signal correlation at this MR contrast (highlighted byarrows 520). For example, neither of these image features can beaffected negatively by the joint reconstruction.

FIG. 4 illustrates a set of images of a prior art (e.g., conventional)inverse Fourier transform-MR and EM-PET reconstruction (e.g., row 405),compared with individual MR and PET nonlinear compressed sensingreconstruction (e.g., row 410), and the exemplary joint imagereconstruction for MR/PET data (e.g., row 415). The improved spatialresolution of the PET data produced by the exemplary system, method andcomputer-accessible medium can be seen in FIG. 4. In particular,superior depiction of the sulcal spaces can be seen in the exemplaryjoint reconstruction results. Also note that this enhancement may not bepresent in the individual CS reconstruction, which can demonstrate thatthe improved resolution can be a consequence of sharing informationbetween the two modalities, not the nonlinear reconstruction in itself

Two axial slices and coronal and sagittal reformats of the experimentswith Cartesian MPRAGE of a brain tumor patient can be performed. FIG. 4shows, fused MR and PET images from conventional inverse Fouriertransform-MR and EM-PET reconstruction (e.g., column 420) compared withindividual MR and PET nonlinear compressed sensing reconstructions(e.g., column 425) and the exemplary system, method, andcomputer-accessible medium reconstruction for MR/PET data (e.g., column420). An improvement in resolution can be observed with the exemplarysystem, method and computer-accessible medium. An interesting feature ofthis particular dataset can be the distinct hyper-intense lesion in MRin the cranial slice (e.g., row 400) where no PET tracer accumulationoccurs. In contrast, the caudal slice (e.g., row 405) includessubcortical gray matter regions (e.g., caudate and thalamus), again withno substantial signal correlation at this MR contrast. For example,neither of these image features can be affected negatively by the jointreconstruction. The position of the cross sectional plot in FIG. 6A isindicated with a dashed arrow 605 in the IFT/EM reconstruction of thecranial slice.

This can be further demonstrated with cross-sectional profile plotsacross this particular lesion (see, e.g., FIG. 6B). Exemplary graphs areshown for jointly reconstructed MRI (curve 610), PET EM (curve 615), PETindividual CS (curve 620) and jointly reconstructed PET (curve 625).While jointly reconstructed PET shows some sharper edges in areas whereMRI also exhibits sharp edges, no systematic bias of the PET signalvalues can be introduced by the joint reconstruction.

While the exemplary results from FIGS. 4 and 5 demonstrate image qualityenhancement for PET using the exemplary system, apparatus, method andcomputer-accessible medium according to an exemplary embodiment of thepresent disclosure, the exemplary joint reconstruction procedure canalso be beneficial for MR data acquisition in cases when MR images canbe reconstructed from undersampled (e.g., accelerated) data sets. FIG. 7shows asset of exemplary image of a pseudorandom one-dimensional (“1D”)subsampling pattern with 3-fold acceleration and corresponding inverseFourier transform (“IFT”) reconstruction, MR-compressed sensingreconstruction and the exemplary joint reconstruction with PET data,according to an exemplary embodiment of the present disclosure. Theexemplary results shown in FIG. 7 can be reconstructed from a 3-foldaccelerated data set using a 1D pseudorandom subsampling pattern inphase encoding (“PE”) direction. Results using a prior art IFTreconstruction, MR-only compressed sensing (see, e.g., Reference 7) andthe exemplary joint reconstruction with PET data are shown. Jointreconstruction results indicate superior sharpness and detectability ofsmall structures using the exemplary system, method andcomputer-accessible medium, as compared to compressed sensing alone.

The exemplary system, method and computer-accessible medium, accordingto an exemplary embodiment of the present disclosure, can providevarious advantages over previous systems as it can treat MR and PET dataas one single dataset during image reconstruction, and it can exploitcorrelations of the underlying anatomy of the two datasets. This canfacilitate the reconstruction of PET images with higher resolution andbetter SNR, and in the exemplary PET reconstruction with MR anatomicalpriors (see, e.g., Reference 8), MR image reconstruction can beperformed as a separate procedure and these images can then be used toenhance PET images. The exemplary system, method and computer-accessiblemedium, according to an exemplary embodiment of the present disclosure,can also operate directly with both MR and PET measurement data. Thiscan also apply to the exemplary motion correction approach from.

Additionally, the exemplary system, method and computer-accessiblemedium according to an exemplary embodiment of the present disclosure,can (i) reconstruct PET images with higher resolution; (ii) reconstructPET images with higher SNR; (iii) provide faster acquisition of both MRand PET data; (iv) improve quantitative assessment; (v) reduce artifactsfrom technical sources and patient motion; and/or (vi) incorporatedynamic correlations into the exemplary joint reconstruction framework.

Additionally, the exemplary system, method and computer accessiblemedium can be used with various other imaging modalities including anoptical imaging modality, Single-photon emission computed tomography(“SPECT”), or any imaging modalities that can share some commonelements.

FIG. 8 is a flow diagram of an exemplary method 800 for generating afirst image and a second image of a tissue according to an exemplaryembodiment of the present disclosure, which can be performed, e.g., byan exemplary system of FIG. 9. For example, at procedure 805,information related to a combination of first imaging information andsecond imaging information as a single data set can be received, whichcan be MR and PET imaging information. At procedure, 810, a number ofdimensions can be generated, and the information can be separated intoat least two dimensions at procedure 815, where at least one first ofthe dimensions can correspond to the first imaging information and whereat least one second of the dimensions can correspond to the secondimaging information. At procedure 820, sharing of information betweenthe first imaging information and second imaging information can besubstantially prevented, and at procedure 825, a sparsity parameter canbe applied to the first imaging information to remove undersamplingartifacts from the first imaging information. At procedure 830, a firstimage and a second image can be generated based on the separatedinformation. At procedure 835 and initial 3D volume can be generatedbased on the second imaging information which can be used to update thesecond image.

FIG. 9 shows a block diagram of an exemplary embodiment of a systemaccording to the present disclosure. For example, exemplary proceduresin accordance with the present disclosure described herein can beperformed by a processing arrangement and/or a computing arrangement902. Such processing/computing arrangement 902 can be, for exampleentirely or a part of, or include, but not limited to, acomputer/processor 904 that can include, for example one or moremicroprocessors, and use instructions stored on a computer-accessiblemedium (e.g., RAM, ROM, hard drive, or other storage device).

As shown in FIG. 9, for example a computer-accessible medium 906 (e.g.,as described herein above, a storage device such as a hard disk, floppydisk, memory stick, CD-ROM, RAM, ROM, etc., or a collection thereof) canbe provided (e.g., in communication with the processing arrangement902). The computer-accessible medium 906 can contain executableinstructions 908 thereon. In addition or alternatively, a storagearrangement 910 can be provided separately from the computer-accessiblemedium 906, which can provide the instructions to the processingarrangement 902 so as to configure the processing arrangement to executecertain exemplary procedures, processes and methods, as described hereinabove, for example.

Further, the exemplary processing arrangement 902 can be provided withor include an input/output arrangement 914, which can include, forexample a wired network, a wireless network, the internet, an intranet,a data collection probe, a sensor, etc. As shown in FIG. 9, theexemplary processing arrangement 902 can be in communication with anexemplary display arrangement 912, which, according to certain exemplaryembodiments of the present disclosure, can be a touch-screen configuredfor inputting information to the processing arrangement in addition tooutputting information from the processing arrangement, for example.Further, the exemplary display 912 and/or a storage arrangement 910 canbe used to display and/or store data in a user-accessible format and/oruser-readable format.

The foregoing merely illustrates the principles of the disclosure.Various modifications and alterations to the described embodiments willbe apparent to those skilled in the art in view of the teachings herein.It will thus be appreciated that those skilled in the art will be ableto devise numerous systems, arrangements, and procedures which, althoughnot explicitly shown or described herein, embody the principles of thedisclosure and can be thus within the spirit and scope of thedisclosure. Various different exemplary embodiments can be used togetherwith one another, as well as interchangeably therewith, as should beunderstood by those having ordinary skill in the art. In addition,certain terms used in the present disclosure, including thespecification, drawings and claims thereof, can be used synonymously incertain instances, including, but not limited to, e.g., data andinformation. It should be understood that, while these words, and/orother words that can be synonymous to one another, can be usedsynonymously herein, that there can be instances when such words can beintended to not be used synonymously. Further, to the extent that theprior art knowledge has not been explicitly incorporated by referenceherein above, it is explicitly incorporated herein in its entirety. Allpublications referenced are incorporated herein by reference in theirentireties.

EXEMPLARY REFERENCES

The following references are hereby incorporated by reference in theirentirety.

-   1. Ralf Ladebeck and Wolfgang Renz. Combined MR/PET system. U.S.    Pat. No. 7,218,112 B2, US 20060293580 Al, CN 1868406 A, CN 100591274    C.-   2. Shepp and Vardi. Maximum Likelihood Reconstruction for Emission    Tomograph. IEEE Trans. Medical Imaging 1: 113-122 (1982).-   3. Duarte, Sarvotham, Baron, Wakin and Baraniuk. Distributed    Compressed Sensing of Jointly Sparse Signals. Conference Record of    the Thirty-Ninth Asilomar Conference on Signals, Systems and    Computers, 1537-1541 (2005).-   4. Hudson and Larkin. Accelerated image reconstruction using ordered    subsets of projection data. IEEE Trans. Medical Imaging, 13: 601-609    (1994).-   5. Daubechies, Defrise and De Mol. An iterative thresholding    algorithm for linear inverse problems with a sparsity constraint.    Communications on Pure and Applied Mathematics 57: 1416-1457 (2004).-   6. Kösters, Schäfers, and Wuebbeling. EMRECON: An expectation    maximization based image reconstruction framework for emission    tomography data. IEEE NSS/MIC: 4365-4368 (2011).-   7. Lustig M, Donoho D, Pauly J M. Sparse MRI: The application of    compressed sensing for rapid MR imaging. Magn Reson Med 58:1182-1195    (2007).-   8. Vunckx, Atre, Baete, Reilhac, Deroose, Van Laere and Nuyts.    Evaluation of three MRI-based anatomical priors for quantitative PET    brain imaging. IEEE Trans. Medical Imaging 31: 599-612 (2012).-   9. Ullisch, Scheins, Weirich, Rota Kops, Celik, Tellmann, Stoecker,    Herzog and Shah. MR-Based PET Motion Correction Procedure for    Simultaneous MR-PET Neuroimaging of Human Brain. PLoS ONE 7(11)    (2012): e48149. doi:10.1371/journal.pone.0048149.

What is claimed is:
 1. A non-transitory computer-accessible mediumhaving stored thereon computer-executable instructions for generating atleast one first image and at least one second image of at least onetissue which are different from one another, wherein, when a computerarrangement executes the instructions, the computer arrangement isconfigured to perform procedures comprising: receiving combinedinformation related to a combination of first imaging information andsecond imaging information data as a single data set; separating thecombined information into at least two dimensions into a separatedinformation, at least one first of the at least two dimensionscorresponding to the first imaging information and at least one secondof the at least two dimensions corresponding to the second imaginginformation; and generating the at least one first image and the atleast one second image based on the separated information.
 2. Thecomputer-accessible medium of claim 1, wherein the first imaginginformation includes magnetic resonance (MR) data, and wherein the atleast one second imaging information includes positron emissiontomography (PET) data.
 3. The computer-accessible medium of claim 2,wherein the at least one first image is at least one MR image, and theat least one second image is at least one PET image.
 4. Thecomputer-accessible medium of claim 1, wherein the at least twodimensions are at least four dimensions.
 5. The computer-accessiblemedium of claim 1, wherein the computer arrangement is furtherconfigured to generate the at least two dimensions based on anoptimization procedure.
 6. The computer-accessible medium of claim 1,wherein the computer arrangement is further configured to at leastsubstantially prevent sharing of the first imaging information and thesecond imaging information with one another when the first imaginginformation and the second imaging information to not match.
 7. Thecomputer-accessible medium of claim 1, wherein the computer arrangementis further configured to apply a sparsity parameter to the first imaginginformation to remove undersampling artifacts from the first imaginginformation.
 8. The computer-accessible medium of claim 1, whereincomputer arrangement is further configured to generate an initialthree-dimensional image volume from the second imaging information basedon an expectation maximization (EM) procedure.
 9. Thecomputer-accessible medium of claim 8, wherein computer arrangement isfurther configured to update the at least one second image using the EMprocedure.
 10. The computer-accessible medium of claim 2, whereincomputer arrangement is further configured to generate an initialestimation of the MR data by applying an adjoint of an MR forwardoperator to the MR data.
 11. The computer-accessible medium of claim 10,wherein the MR data include measured k-space raw data.
 12. Thecomputer-accessible medium of claim 1, wherein the first imaginginformation is associated with a first imaging modality, and the secondimaging information is associated with a second imaging modality that isdifferent from the first imaging modality.
 13. The computer-accessiblemedium of claim 12, wherein the first imaging modality is at least oneof a magnetic resonance imaging modality, a positron emission tomographymodality, a single-photon emission computed tomography modality, or anoptical imaging modality.
 14. The computer-accessible medium of claim12, wherein the second imaging modality is at least one of a magneticresonance imaging modality, a positron emission tomography modality, asingle-photon emission computed tomography modality or an opticalimaging modality.
 15. The computer-accessible medium of claim 1, whereinthe computer arrangement is further configured to generate the at leastone first image and the at least one second image based on anincoherence of artifacts in the separated information.
 16. Thecomputer-accessible medium of claim 1, wherein the computer arrangementis further configured to generate the at least one first image and theat least one second image based on a comparison of the separatedinformation.
 17. The computer-accessible medium of claim 1, wherein thecomputer arrangement is further configured to generate the at least onefirst image temporally before the at least one second image.
 18. Thecomputer-accessible medium of claim 17, wherein the computer arrangementis further configured to generate the at least one second image based onthe at least one first image.
 19. A method for generating at least onefirst image and at least one second image of at least one tissue whichare different from one another, comprising: receiving combinedinformation related to a combination of first imaging information andsecond imaging information as a single data set; separating the combinedinformation into at least two dimensions into separated information, atleast one first of the at least two dimensions corresponding to thefirst imaging information and at least one second of the at least twodimensions corresponding to the second imaging information; and using acomputer hardware arrangement, generating the at least one first imageand the at least one second image based on the separated information.20. A system for generating at least one first image and at least onesecond image of at least one tissue which are different from oneanother, comprising: a computer hardware arrangement configured to:receive combined information related to a combination of first imaginginformation and second imaging information as a single data set;separate the combined information into at least two dimensions intoseparated information, at least one first of the at least two dimensionscorresponding to the first imaging information and at least one secondof the at least two dimensions corresponding to the second imaginginformation; and generate the at least one first image and the at leastone second image based on the separated information.